Is dysphemism the same as swearing?

Yes: swearing involves using profane vocabulary; dysphemism involves negative, offensive terms for particular things. You can swear without dysphemisms, and indeed without having any negativity at all, through the use of profanities as positive intensifiers:

That was a motherfucking magnificent job!

Holy fucking shit, that felt good!

Jesus, that guy’s a clever cunt. (That’s more a Commonwealth thing)

Can you use dysphemisms without swearing?

Yes, though it’s subtle: dysphemism is using a term that is offensive in some way, but there’s a lot of wiggle room in how. We just saw that the term can be offensive in general, but not in the particular context—like the examples above. We can also have a term that is offensive ONLY in that context.

Example? Wikipedia has an excellent one. In many cultures, using a proper name for your elders is disrespectful, and hence gives offence: it’s a dysphemism. Hey Janice, where’s lunch? instead of Hello mother, where is lunch? But it isn’t swearing: it isn’t the same as Hey bitch, where’s my food? There’s nothing profane in itself about the name Janice.